1. Field of the Invention
The invention relates generally to devices for improving the skills of musicians and more particularly to devices which improve a musician's intonation, that is, the ability of the musician to play a note at the proper pitch.
2. Description of Related Art: FIGS. 1 and 2
The notes musicians play or sing belong to scales. There are many kinds of possible scales; in the one used in Western music, the scale is divided into octaves, with a note that is an octave higher than a given note having exactly twice the frequency of the given note. An octave has 12 notes in it; thus, if the note on which the octave begins (this note is the fundamental), is a C, the notes in the octave are C, C#, D, D#, E, F, F#, G, G#, A, A#, B. This particular scale is called a C chromatic scale. Scales are characterized as belonging to particular keys. A key specifies the fundamental of a scale and the relationship between the notes of the chromatic scale and the intervals of the key. An interval specifies the relationship of the pitch in the key's scale to the pitch of the key's fundamental. A key's name specifies the scale's fundamental and whether the scale is major or minor. The intervals of a major scale are the major second, the major third, the fourth, the fifth, the major sixth, and the major seventh. The key of C major, for example has C as its fundamental and includes the following notes of the C chromatic scale. The interval is in parentheses following the note: C, D(major second), E (major third), F (perfect fourth), G (perfect fifth), A (major sixth), B (major seventh), C (perfect octave).
The intervals of a natural minor scale include the major second, minor third, perfect fourth, perfect fifth, minor sixth, and minor seventh; the key of C minor again has C as its fundamental and includes the following notes of the C chromatic scale: C, D, Eb, F, G, Ab, Bb, C. Important intervals for the present discussion are the minor and major third and the fifth. The perfect fifth may be augmented (C-G# in the key of C major) or diminished (C-Gb).
The actual pitches of the notes in a scale are determined by whether the scale is a just scale or a tempered scale. In a just scale, the ratios between the frequencies of the notes in the scale and the frequency of the fundamental are rational numbers. This is shown in FIG. 1. In table 101, there is a row 102(i) in table 101 for each interval; column 103 indicates the row's interval; column 105 shows the ratio of the frequencies of the pitches specified by the interval. A property of just scales is that the pitches of the notes in a key differ slightly from corresponding notes in other keys; for example, the pitch of G in a just C major scale is slightly different from the pitch of G in a just F major scale.
These slight differences between the pitches of the notes in the just scales cause no problems for singers, players of most string instruments, and players of wind instruments, since they can easily adjust the intonation of the notes they sing or play to fit whatever just key they are singing or playing in. There is thus no need for a string or wind player to retune his or her instrument when the key changes. That is not the case with fretted string instruments or keyboard instruments such as harpsichords or pianos. With these instruments, the player cannot adjust the intonation of a string without returning the instrument, and consequently, if the instrument is tuned to the just scale for a key, only music in that key will sound good when played on the instrument. A key change requires that the instrument be returned, and for keyboard instruments, that is a considerable undertaking.
Keyboard instruments become capable of playing music in all keys when they are tuned with a tempered scale. The tempered scale does not sound as good as the just scale for any particular key, but it sounds reasonable in all keys. There are various historical systems for tempering the scales of keyboard instruments. The systems are termed temperaments. The tempering system used in modern keyboard instruments is the equal temperament system. Col. 107 of FIG. 1 compares the ratios between the fundamental and the intervals in the equal temperament system with the ratios used in the just scale. Table 201 of FIG. 2 again has a row 203(i) for each interval. The intervals are specified in col. 205. Table 201 compares the frequencies of the notes of a just scale in the key of C (col. 207) with the frequencies of the pitches of the scale beginning at C for a piano that has been tuned according to the equal temperament system (col. 209). Col. 211 gives the difference in Hz between the frequencies of the corresponding notes.
When a keyboard instrument is part of an ensemble, all of the other singers or players must of course adjust to the tempered scale of the keyboard instrument. Otherwise, however, singers and instrumentalists can use the just scale for the key they are currently playing in. The challenge here is developing the intonation skills necessary to correctly play the notes in the just scales for each key. Where there is a correct source for a pitch, a player of a string or wind instrument can determine the quality of his or her intonation by listening for the beat that is produced when two notes having almost the same frequency are sounded together. As the difference between the frequencies of the notes get smaller, the beat gets slower and finally vanishes. Similarly, if a player is playing a note in a chord and the intonation of the note is not correct relative to the other notes in the chord, a beat is produced Again, when the note is played with the correct intonation, no beat is heard.
The phenomenon of beats when a note in a chord is played out of tune has long been used in intonation training, and there are existing intonation training devices that take advantage of the phenomenon. One class of such devices is CDs whose tracks contain chords of pitches belonging to a just scale. In the following discussion, a chord is understood to mean the sound produced by the simultaneous sounding of two or more distinct pitches in a scale. A chord whose pitches belong to a just scale is termed in the following a pure chord. The player who wants to develop his or her intonation selects a track with the desired pure chord and then plays along with the track, adjusting his or her intonation as required to eliminate the beat. The inventor of the present invention has been producing and selling such a CD, called The Tuning CD, since 1998. The Tuning CD is available from The Tuning CD, P.O. Box 1703, Cherry Hill, N.J. 08034-0090. A description of this CD can be found at www.thetuningcd.com; in the Tuning CD, the chords are pure open fifths.
Another example of a CD for intonation training is produced by TuneUp Systems, PO Box 29574, Richmond, Va. 23242. A description of this CD could be found in May, 2004 at www.tuneupsystems.com/website—002.htm
Another class of intonation training devices is software that runs on personal computers. A modern personal computer of course includes an audio synthesizer, and when the computer provides digital inputs to the sound board that specify an audio signal to the audio synthesizer, the audio synthesizer generates an audio signal as specified by the inputs. Intonation training software is thus able to cause the audio synthesizer to generate pure chords for intonation training. Examples of such software include the SmartMusic Intonation Trainer, available from MakeMusic, Inc, and the Z-Tuner, available from Jumatek, Inc. A description of the SmartMusic Intonation Trainer software could be found in May, 2004 at www.mccormicksnet.com/intonatn.htm and a description of the Z-Tuner could be found at www.jumatek.com/ztuner.htm
While the CD-based and software-based intonation training devices are perfectly capable of producing the pure chords needed for intonation training, they do have practical drawbacks. To begin with, the devices are not particularly portable. For the CD, you need a CD player; for the software, you need a PC, and even the smallest CD players and laptop PCs are not pocket size. Then there is the matter of the user interface: to use the CD, you need to know which track has which key, and for that you need a description of what's on the CD as well as the CD. The intonation training software has the usual problem with software—namely, it can do anything the user wants, but configuring it to do it is difficult and requires familiarity with the software and with the graphical user interface presented by a modem PC operating system. For example, both the SmartMusic Intonation Trainer and the Z-Tuner provide just scales and can be made to produce chords using pitches of a just scale, but it is up to the user to define for each key the chords he or she wants to use for intonation practice. What is needed, and what is provided by the present invention, is an intonation training device that's as compact, portable, and easy to use as the electronic devices that have long been used to tune musical instruments. It is an object of the present invention to provide such an intonation training device.